when responding thank you in email, do I need to address with "dear" again?

If they're using 'dear', you should do likewise.

If they've signed off with their first name and surname, you can move to 'dear firstname' rather than 'dear mr/mrs surname'

You don't use "dear" in email. Ever. You do that in letters. You can start off with the person's name, if you know it, or just state your message. In this case "Thank you for your help" is quite sufficient. I actually get a little annoyed when students insist on writing back with "thank you" since it's another message flooding my inbox, and another message I have to open and read. But you can do it if you want to. It won't affect your admissions decision in the U.S.

Since it's pretty formal, go ahead and keep it up I'd say.

I often don’t. I don’t think it’s necessary.